This paper describes an experimental investigation of a buoyant, m*<1, tethered cylinder which is free to move in an arc about its pivot points. The response of the cylinder, in particular its layover angle and flow-induced motion, is considered for a range of flow velocities and mass ratios. At pertinent parameters, the flow fields were also measured using particle image velocimetry (PIV). At lower mass ratios, 0.54≤m*≤0.72, two distinct states are observed, the low-amplitude and upper states. The transition from the low-amplitude state to the upper state is characterized by abrupt jumps in the amplitude of oscillation, the mean tether angle and the drag coefficient as well as distinct changes in the cylinder's wake. At higher mass ratios, the jump does not occur; however, as m* approaches unity at low flow velocities the cylinder's motion is more periodic than that observed at lower m*. The flow fields indicate that the low-amplitude state exhibits a 2S Kármán wake. The wake of the upper state has long shear layers extending well across the wake centreline, is not fully symmetric and is often consistent with either the 2P or P+S shedding modes. There is a collapse of the response data, in particular an excellent collapse of the mean layover angle, when the response parameters are plotted against the buoyancy Froude number, Frbuoyancy=U/((1-m*) gD)0.5. When the data collapses, the two states described above are clearly delineated.

The linear stability of variable viscosity, miscible core–annular flows is investigated. Consistent with pipe flow of a single fluid, the flow is stable at any Reynolds number when the magnitude of the viscosity ratio is less than a critical value. This is in contrast to the immiscible case without interfacial tension, which is unstable at any viscosity ratio. Beyond the critical value of the viscosity ratio, the flow can be unstable even when the more viscous fluid is in the core. This is in contrast to plane channel flows with finite interface thickness, which are always stabilized relative to single fluid flow when the less viscous fluid is in contact with the wall. If the more viscous fluid occupies the core, the axisymmetric mode usually dominates over the corkscrew mode. It is demonstrated that, for a less viscous core, the corkscrew mode is inviscidly unstable, whereas the axisymmetric mode is unstable for small Reynolds numbers at high Schmidt numbers. For the parameters under consideration, the switchover occurs at an intermediate Schmidt number of about 500. The occurrence of inviscid instability for the corkscrew mode is shown to be consistent with the Rayleigh criterion for pipe flows. In some parameter ranges, the miscible flow is seen to be more unstable than its immiscible counterpart, and the physical reasons for this behaviour are discussed.

A detailed parametric study shows that increasing the interface thickness has a uniformly stabilizing effect. The flow is least stable when the interface between the two fluids is located at approximately 0.6 times the tube radius. Unlike for channel flow, there is no sudden change in the stability with radial location of the interface. The instability originates mainly in the less viscous fluid, close to the interface.

This paper contains data on and insights into the origins of turbulence associated with a partial blockage at the exit of a two-dimensional, laminar, horizontal duct flow. In essence, this is the upstream approach region of the forward-facing step problem. This work was motivated by the need to identify and control unsteady streamwise vortices generated in the headbox (i.e. contraction section) of an industrial paper machine. The duct was 57.2 cm wide × 10.16 cm high, with up to a 50 % blockage. Experiments were scaled to match Reynolds numbers found in paper machines; exit velocities were as large as 200 cm s−1. The goal of the research was to map the flow at the exit and to examine the response of the flat-plate turbulent boundary layer on the opposing wall under the partial blockage. Laser-induced fluorescence (LIF) and digital particle image velocimetry (DPIV) were used to examine flow in three orthogonal planes at various stations upstream of the duct exit. Mean and instantaneous DPIV vector fields clearly show that an unsteady spanwise vortex forms in the corner formed by the top nozzle wall and partial blockage which, in turn, gives rise to turbulent streamwise vortices.

A turbulent boundary layer was initiated on the duct wall opposite the blockage, upstream of a two-dimensional contraction. Results show that even though the acceleration parameter, K, exceeded the nominal critical level of 3.0 × 10−6 for relaminarization beneath the blockage, the flow did not reach a quasi-laminar state. In addition, there did not appear to be direct interaction between unsteady vortex formation at the partial blockage on the upper wall and bottom-wall turbulent boundary layer structures.

Three-dimensional stability of the periodic wake of tightly packed rotated and inline cylinder arrays is investigated for 60 ≤ Re ≤ 270. Results are compared with existing numerical and experimental studies for an isolated cylinder. Numerical Floquet analysis shows that the two-dimensional wakes of the rotated and inline arrays with spacing P/D = 1.5 become unstable at Rec = 64 ± 0.5 and Rec = 132 ± 1 respectively. Two-dimensional vortex shedding flow is unlikely in practice for such flows. The dominant spanwise wavelength is λ/D = 0.9 ± 0.1 for the rotated array at Re = 100 and λ/D = 3.0 ± 0.1 for the inline array at Re = 200. Three-dimensional simulations show excellent agreement with the Floquet analysis for the rotated case, and reasonable agreement for the inline case. The instability mechanism appears to be similar to Mode A for an isolated cylinder, although the structure of the three-dimensional vorticity is different due to the spatial periodicity of the flow. Unlike the isolated cylinder, both array flows are unstable as λ → ∞ (like a thin shear layer). This is the first investigation of three-dimensional wake instability in cylinder arrays, a problem of significant practical and theoretical interest.

Three-dimensional spectral/hp computations have been performed to study the fundamental mechanisms of vortex shedding in the wake of curved circular cylinders at Reynolds numbers of 100 and 500. The basic shape of the body is a circular cylinder whose centreline sweeps through a quarter section of a ring and the inflow direction lies on the plane of curvature of the quarter ring: the free stream is then parallel to the geometry considered and the part of the ring that is exposed to it will be referred to as the ‘leading edge’. Different configurations were investigated with respect to the leading-edge orientation. In the case of a convex-shaped geometry, the stagnation face is the outer surface of the ring: this case exhibited fully three-dimensional wake dynamics, with the vortex shedding in the upper part of the body driving the lower end at one dominant shedding frequency for the whole cylinder span. The vortex-shedding mechanism was therefore not governed by the variation of local normal Reynolds numbers dictated by the curved shape of the leading edge. A second set of simulations were conducted with the free stream directed towards the inside of the ring, in the so-called concave-shaped geometry. No vortex shedding was detected in this configuration: it is suggested that the strong axial flow due to the body's curvature and the subsequent production of streamwise vorticity plays a key role in suppressing the wake dynamics expected in the case of flow past a straight cylinder. The stabilizing mechanism stemming from the concave curved geometry was still found to govern the wake behaviour even when a vertical extension was added to the top of the concave ring, thereby displacing the numerical symmetry boundary condition at this point away from the top of the deformed cylinder. In this case, however, the axial flow from the deformed cylinder was drawn into the wake of vertical extension, weakening the shedding process expected from a straight cylinder at these Reynolds numbers. These considerations highlight the importance of investigating flow past curved cylinders using a full three-dimensional approach, which can properly take into account the role of axial velocity components without the limiting assumptions of a sectional analysis, as is commonly used in industrial practice. Finally, towing-tank flow visualizations were also conducted and found to be in qualitative agreement with the computational findings.

In this paper we investigate the interaction between two corotating quasi-geostrophic vortices. The initially ellipsoidal vortices are separated horizontally by a distance corresponding to the margin of stability, as determined from an ellipsoidal analysis. The subsequent interaction depends on four parameters: the vortex volume ratio, the vertical centroid separation, and the height-to-width aspect ratios of each vortex. The most commonly observed strong interaction is partial merger, where only part of the weaker vortex is incorporated into the stronger one or cast into filamentary debris. Despite the proliferation of small-scale filamentary structure during many vortex interactions, on average the self-induced vortex energy exhibits an ‘inverse cascade’ to larger scales, broadly consistent with spectral theories of turbulence. Curiously, we observe that a range of intermediate-scale vortices are preferentially sheared out during the interactions, leaving two main populations of large and small vortices.

Two-layer exchange flows are observed in the channels/straits connecting two water bodies of different densities. This study examines the nature of the barotropic forcing and its effect on the interfacial waves in two-layer exchange flows over a smooth/break underwater sill. Experiments were conducted with different initial conditions, distinguishing the case of hydrostatic disequilibrium and the case of a global pressure-balanced state. The experiments demonstrate that the baroclinic exchange flow is dominated by the barotropic-forcing-induced oscillations. A simplified barotropic model is developed to predict the period of the barotropic oscillation with an excellent agreement with experimental measurements. Detailed velocity and flow-rate measurements also indicate the importance of the barotropic forcing in exchange flows. The effect of the superimposed barotropic forcing on the interfacial wave characteristics is also investigated. Large two-dimensional surge-like structures are observed during the experiments, whose generation is shown to be related to the flow-rate oscillations. The length scales of these structures is comparable with the total water depth and is shown to increase with increasing Reynolds numbers.

An extended lattice Boltzmann model is developed for simulating the convection–diffusion phenomena associated with solid–liquid phase transition processes. Macroscopic hydrodynamic variables are obtained through the solution of an evolution equation of a single-particle density distribution function, whereas, the macroscopic temperature field is obtained by solving auxiliary scalar transport equations. The novelty of the present methodology lies in the formulation of an enthalpy-based approach for phase-change modelling within a lattice-Boltzmann framework, in a thermodynamically consistent manner. Thermofluidic aspects of phase transition are handled by means of a modified enthalpy–porosity formulation, in conjunction with an appropriate enthalpy-updating closure scheme. Lattice-Boltzmann simulations of melting of pure gallium in a rectangular enclosure, Rayleigh–Bénard convection in the presence of directional solidification in a top-cooled cavity, and crystal growth during solidification of an undercooled melt agree well with the numerical and experimental results available in the literature, and provide substantial evidence regarding the upscaled computational economy provided by the present methodology.

A viscosity stratification is considered as a possible mean to postpone the onset of transition to turbulence in channel flow. As a prototype problem, we focus on the linear stability of shear-thinning fluids modelled by the Carreau rheological law. To assess whether there is stabilization and by how much, it is important both to account for a viscosity disturbance in the perturbation equations, and to employ an appropriate viscosity scale in the definition of the Reynolds number. Failure to do so can yield qualitatively and quantitatively incorrect conclusions. Results are obtained for both exponentially and algebraically growing disturbances, demonstrating that a viscous stratification is a viable approach to maintain laminarity.

The existence of trapped edge waves in a rotating stratified fluid with non-constant topography is studied using asymptotic and numerical techniques. A refinement of the classical WKBJ method is employed that is uniform at both the shoreline and caustic, where the classical approximation is singular, and is also uniform over long distances from the shore. This approach requires the use of comparison equations and it is shown that the two used previously in the literature are asymptotically equivalent in terms of the wave amplitude, but have small differences in the predicted wave frequencies. These asymptotic results, and results using shallow-water theory, are then compared to results from a careful numerical study of the nonlinear differential eigenvalue problem, allowing their range of practical applicability to be assessed. This numerical approach is also used to investigate whether trapping occurs in non-trivial and realistic geometries in the internal gravity wave band, which has been an open question for some time.

The effect of Prandtl number on the linear stability of a plane thermal plume is analysed under quasi-parallel approximation. At large Prandtl numbers (Pr > 100), we found that there is an additional unstable loop whose size increases with increasing Pr. The origin of this new instability mode is shown to be tied to the coupling of the momentum and thermal perturbation equations. Analyses of the perturbation kinetic energy and thermal energy suggest that the buoyancy force is the main source of perturbation energy at high Prandtl numbers that drives this instability.

A computational investigation, supported by a theoretical analysis, is performed to investigate a pressure-driven flow around a line of equispaced spheres moving at a prescribed velocity along the axis of a circular tube. This fundamental study underpins a range of applications including physiological circulation research. A spectral-element formulation in cylindrical coordinates is employed to solve for the incompressible fluid flow past the spheres, and the flows are computed in the reference frame of the translating spheres.

Both the volume flow rate relative to the spheres and the forces acting on each sphere are computed for specific sphere-to-tube diameter ratios and sphere spacing ratios. Conditions at which zero axial force on the spheres are identified, and a region of unsteady flow is detected at higher Reynolds numbers (based on tube diameter and sphere velocity). A regular perturbation analysis and the reciprocal theorem are employed to predict flow rate and drag coefficient trends at low Reynolds numbers. Importantly, the zero drag condition is well-described by theory, and states that at this condition, the sphere velocity is proportional to the applied pressure gradient. This result was verified for a range of spacing and diameter ratios. Theoretical approximations agree with computational results for Reynolds numbers up to O(100).

The geometry dependence of the zero axial force condition is examined, and for a particular choice of the applied dimensionless pressure gradient, it is found that this condition occurs at increasing Reynolds numbers with increasing diameter ratio, and decreasing Reynolds number with increasing sphere spacing.

Three-dimensional simulations and predictions of a Floquet linear stability analysis independently elucidate the bifurcation scenario with increasing Reynolds number for a specific diameter ratio and sphere spacing. The steady axisymmetric flow first experiences a small region of time-dependent non-axisymmetric instability, before undergoing a regular bifurcation to a steady non-axisymmetric state with azimuthal symmetry m = 1. Landau modelling verifies that both the regular non-axisymmetric mode and the axisymmetric Hopf transition occur through a supercritical (non-hysteretic) bifurcation.

Turbulence measurements for rough-wall boundary layers are presented and compared to those for a smooth wall. The rough-wall experiments were made on a woven mesh surface at Reynolds numbers approximately equal to those for the smooth wall. Fully rough conditions were achieved. The present work focuses on turbulence structure, as documented through spectra of the fluctuating velocity components, swirl strength, and two-point auto- and cross-correlations of the fluctuating velocity and swirl. The present results are in good agreement, both qualitatively and quantitatively, with the turbulence structure for smooth-wall boundary layers documented in the literature. The boundary layer is characterized by packets of hairpin vortices which induce low-speed regions with regular spanwise spacing. The same types of structure are observed for the rough- and smooth-wall flows. When the measured quantities are normalized using outer variables, some differences are observed, but quantitative similarity, in large part, holds. The present results support and help to explain the previously documented outer-region similarity in turbulence statistics between smooth- and rough-wall boundary layers.

We present new insights and results for the problem of a film falling down a heated wall: (i) treatment of a mixed heat flux boundary condition on the substrate; (ii) development of a long-wave theory for large Péclet numbers; (iii) refined treatment of the energy equation based on a high-order Galerkin projection in terms of polynomial test functions which satisfy all boundary conditions; (iv) time-dependent computations for the free-surface height and interfacial temperature; (v) numerical solution of the full energy equation; (vi) demonstration of the existence of a thermal boundary layer at the front stagnation point of a solitary pulse; (vii) development of models that prevent negative temperatures and are in good agreement with the numerical solution of the full energy equation.

One-point statistics of velocity gradients and Eulerian and Lagrangian accelerations are studied by analysing the data from high-resolution direct numerical simulations (DNS) of turbulence in a periodic box, with up to 40963 grid points. The DNS consist of two series of runs; one is with kmaxη ~ 1 (Series 1) and the other is with kmaxη ~ 2 (Series 2), where kmax is the maximum wavenumber and η the Kolmogorov length scale. The maximum Taylor-microscale Reynolds number Rλ in Series 1 is about 1130, and it is about 675 in Series 2. Particular attention is paid to the possible Reynolds number (Re) dependence of the statistics. The visualization of the intense vorticity regions shows that the turbulence field at high Re consists of clusters of small intense vorticity regions, and their structure is to be distinguished from those of small eddies. The possible dependence on Re of the probability distribution functions of velocity gradients is analysed through the dependence on Rλ of the skewness and flatness factors (S and F). The DNS data suggest that the Rλ dependence of S and F of the longitudinal velocity gradients fit well with a simple power law: S ~ −0.32Rλ0.11 and F ~ 1.14Rλ0.34, in fairly good agreement with previous experimental data. They also suggest that all the fourth-order moments of velocity gradients scale with Rλ similarly to each other at Rλ > 100, in contrast to Rλ < 100. Regarding the statistics of time derivatives, the second-order time derivatives of turbulent velocities are more intermittent than the first-order ones for both the Eulerian and Lagrangian velocities, and the Lagrangian time derivatives of turbulent velocities are more intermittent than the Eulerian time derivatives, as would be expected. The flatness factor of the Lagrangian acceleration is as large as 90 at Rλ ≈ 430. The flatness factors of the Eulerian and Lagrangian accelerations increase with Rλ approximately proportional to RλαE and RλαL, respectively, where αE ≈ 0.5 and αL ≈ 1.0, while those of the second-order time derivatives of the Eulerian and Lagrangian velocities increases approximately proportional to RλβE and RλβL, respectively, where βE ≈ 1.5 and βL ≈ 3.0.

An analysis is made of sound generation by aerodynamic sources near an acoustically compact body (or compact surface feature on a large boundary) that can deform in an arbitrary manner. It is shown how such problems can be investigated by simple extension of the compact Green's function used in the treatment of compact rigid bodies. It is known that this method can furnish rapid and accurate predictions of sound generated by flows with extensive, non-compact distributions of sources in cases where a numerical treatment requires at best tens or hundreds of hours of CPU time. Illustrative applications are made to study (i) the sound generated by a nominally rigid circular lamina of time-dependent radius held in an irrotational mean stream, and (ii) the production of voiced speech by vorticity interacting with a simple model of the vocal folds. In case (ii), it appears that predictions are represented well by a quasi-static approximation that permits the particular results of this paper and previous investigations to be generalized to arbitrarily configured folds.

This paper considers a finite number of rigid bodies moving in potential flow. The dynamics of the solid--fluid system is described in terms of the solid variables only using Kirchhoff potentials. The equations of motion are first derived for the problem of two submerged bodies where one is forced into periodic oscillations. The hydrodynamic coupling causes the free body to drift away from or towards the oscillating body. The method of multiple scales is used to separate the slow drift from the fast response. Interestingly, the free body, when attracted towards the forced one, starts to drift away after it reaches certain separation distance. This suggests that the hydrodynamic coupling helps in preventing collisions. The fluid's role in collision avoidance and motion coordination is examined further through examples. In particular, we show that a free body can coordinate its motion with that of its neighbours, which may be relevant to understanding the coordinated motion in fish schooling.

The merging of a pair of symmetric, horizontally oriented vortices in unstratified and stably stratified viscous fluid is investigated. Two-dimensional numerical simulations are performed for a range of flow conditions. The merging process is resolved into four phases of development and key underlying physics are identified. In particular, the deformation of the vortices, explained in terms of the interaction of vorticity gradient, ∇ω, and rate of strain, S, leads to a tilt in ω contours in the vicinity of the center of rotation (a hyperbolic point). In the diffusive/deformation phase, diffusion of the vortices establishes the interaction between ∇ω and mutually induced S. During the convective/deformation phase, induced flow by filaments and, in stratified flow, baroclinically generated vorticity (BV), advects the vortices thereby modifying S, which, in general, may enhance or hinder the development of the tilt. The tilting and diffusion of ω near the center hyperbolic point causes ω from the core region to enter the exchange band where it is entrained. In the convective/entrainment phase, the vortex cores are thereby eroded and ultimately entrained into the exchange band, whose induced flow becomes dominant and transforms the flow into a single vortex. The critical aspect ratio, associated with the start of the convective/entrainment phase, is found to be the same for both the unstratified and stratified flows. In the final diffusive/axisymmetrization phase, the flow evolves towards axisymmetry by diffusion. In general, the effects of stratification depend on the ratio of the diffusive time scale (growth of cores) to the turnover time (establishment of BV), i.e. the Reynolds number. A crossover Reynolds number is found, above which convective merging is accelerated with respect to unstratified flow and below which it is delayed.

Binary encounters between spherical particles in shear flow are studied for a system bounded by a single planar wall or two parallel planar walls under creeping flow conditions. We show that wall proximity gives rise to a new class of binary trajectories resulting in cross-streamline migration of the particles. The spheres on these new trajectories do not pass each other (as they would in free space) but instead they swap their cross-streamline positions. To determine the significance of the wall-induced particle migration, we have evaluated the hydrodynamic self-diffusion coefficient associated with a sequence of uncorrelated particle displacements due to binary particle encounters. The results of our calculations quantitatively agree with the experimental value obtained by Zarraga & Leighton (Phys. Fluids, vol. 14, 2002, p. 2194) for the self-diffusivity in a dilute suspension of spheres undergoing shear flow in a Couette device. We thus show that the wall-induced cross-streamline particle migration is the source of the anomalously large self-diffusivity revealed by their experiments.

We discuss how large-eddy simulation (LES) can be properly employed to predict the statistics of the resolved velocity fluctuations in shear turbulence. To this purpose an a posteriori comparison of LES data against filtered direct numerical simulation (DNS) is used to establish the necessary conditions that the filter scale LF must satisfy to achieve the preservation of the statistical properties of the resolved field. In this context, by exploiting the physical role of the shear scale LS, the Kármán–Howarth equation allows for the assessment of LES data in terms of scale-by-scale energy production, energy transfer and subgrid energy fluxes. Even higher-order statistical properties of the resolved scales such as the probability density function of longitudinal velocity increments are well reproduced, provided the relative position of the filter scale with respect to the shear scale is properly selected. We consider here the homogeneous shear flow as the simplest non-trivial flow which fully retains the basic mechanism of turbulent kinetic energy production typical of any shear flow, with the advantage that spatial homogeneity implies a well-defined value of the shear scale while numerical difficulties related to resolution requirements in the near wall region are avoided.